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RubiksCube77
Nov Member 2021

RubiksCube77

Posts: 943 Gold Posts by user Forum Profile RuneMetrics Profile
Deriving the formula for escape speed
We will use the conservation of energy
Kf-Uf=Ki-Ui
K (kinetic energy) = (1/2)m1v^2 (m1=mass v=velocity of object)
U (potential energy) = (Gm1m2)/r (G=gravitational constant m2=mass of planet r=distance from center of planet)
Eventually the object will be very far away from the planet so r(final) is infinity so Limit as x approaches infinity of (1/x)=0 and in this case Uf is 0.
I don't exactly remember the reasons why v(final) is zero, but anything multiplied by 0 is 0, so Kf is 0.
0-0=Ki-Ui
Ki=Ui
(1/2)m1v^2= (Gm1m2)/r
(1/2)v^2= (Gm2)/r
v^2= (2Gm2)r
v= ((2Gm2)/r)^(1/2) is the formula for escape speed on a planet

Escape speed on earth
G (gravitational constant)= 6.67x10^(-11) ((Nm^2)/(kg^2))
m2 (mass of Earth)=5.98x10^24kg
r (radius of Earth)=6.37x10^6 m

We plug this information into the formula above and we get
v(escape)= 11190.73961 m/s
that is roughly 11200m/s

If anyone spots an error, let me know. I've only taken up for electromagnetism for physics.
I wanted to post here earlier, but was busy with school, so best of luck to this thread. Make RuneScape Great Again usually on at 3:00 PM PST
I am the Emperor of Africa, Afrikaneer Engineer, and retired RSOF troll
The Real Bad African (shenanigans moved to YT under an assumed name)

26-Mar-2015 19:23:10

Mahtavata

Mahtavata

Posts: 4,115 Adamant Posts by user Forum Profile RuneMetrics Profile
Why are there no freaking subscript & superscript options for forums?

Anyway, when reducing your formula, show your work more, since physics profs are nitpicky AF and want like free body diagrams for everything.

What I would've done to find the escape speed formula thingy is...

(1/2)m1v^2= (Gm1m2)/r
(2/1)[(1/2)m1v^2]= [(Gm1m2)/r](2/1)
m1v^2 =( 2Gm1m2)/r
(1/ m1 )[ m1 v^2]=[(2G m1 m2)/r](1/ m1 )
v^2 = (2Gm2)/r
squarerootthat****up(v^2) = squarerootthat****up[(2Gm2)/r]
v = [(2Gm2)/r)^(1/2)]

Basically the same thing, but more work shown, so profs won't take off points over nothing. I'll think about plugging stuff into the formula & doing unit conversions on the forums...which takes forever to type out, but so far what you did looks good.

P.S. Dudes who wear makeup look good.

Edited: for G typos. Yo, give it up g.
Musta.

26-Mar-2015 20:21:18 - Last edited on 26-Mar-2015 20:44:10 by Mahtavata

RubiksCube77
Nov Member 2021

RubiksCube77

Posts: 943 Gold Posts by user Forum Profile RuneMetrics Profile
Thanks for your input Mahtavata.

Luckily for me, my physics teachers weren't that strict, and the steps I did to arrive at my answer sufficed.

My current plans are to major in Mechanical engineering, but I do have a growing interest in mechatronics and the sad thing is that only a few schools in America actually have a mechatronics program from what I heard. Whatever the case is, my ultimate goal is to become a Weapons engineer.

P.S. I'm straight and I like normal women Make RuneScape Great Again usually on at 3:00 PM PST
I am the Emperor of Africa, Afrikaneer Engineer, and retired RSOF troll
The Real Bad African (shenanigans moved to YT under an assumed name)

26-Mar-2015 23:04:07

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27-Mar-2015 16:15:47

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